## Bielefeld-Münster Seminar on## Groups, Geometry and Topology## Wednesday, February 8, 2023. |

#### Talks:

- 10:00 Daniel Keppeler (Münster)
*Automatic continuity for graph products* - 11:30 Amandine Escalier (Münster)
*An overview on Local-to-Global rigidity* - 14:00 Jonas Flechsig (Bielefeld)
*Orbifold mapping class groups and orbifold braid groups* - 15:30 Bianca Marchionna (Bielefeld)
*Trees, buildings and their interactions*

*Abstract:*
The automatic continuity problem asks the following question: Given two topological groups
*G* and *H* and an algebraic homomorphism *f* between those, what are conditions
on the groups *G* and *H*, such that *f* is automatically continuous?
In this talk, we will give an introduction to this problem, where *G* is topologically rich
(e.g. locally compact or Čech complete) and
*H* is a discrete geometric group and in particular a graph product of groups.

11:00 Coffee break

*Abstract:*
We say that a graph *G* is Local-to-Global rigid if there exists *R>0* such that every other graph whose balls of
radius *R* are isometric to the balls of radius *R* in *G* is covered by *G*.
In this talk we provide an overview of this rigidity notion, using buildings as a background scene.
We’ll talk about the motivations, discuss numerous examples and borrow topological tools to settle
the basis. In a second part, we will see the known cases where LG-rigidity is invariant under
quasi-isometry and discuss some strategies to prove this invariance.

You can download the slides
and written notes.

12:30 Lunch break

*Abstract:*
A useful approach to study Artin's braid group *B _{n}* is its identification with the mapping class group

*Map(D*of a disk

_{n})*D*with

*n*marked points. An isomorphism from

*Map(D*to

_{n})*B*is given by evaluation of certain isotopies. In my talk I want to discuss an orbifold analogue. Therefore I will introduce orbifold braid groups and orbifold mapping class groups. In contrast to the classical analogue the evaluation map from the orbifold mapping class group onto the orbifold braid group has a non-trivial kernel. This has surprising consequences for the structure of the pure orbifold braid groups.

_{n}15:00 Coffee break

*Abstract:*
It is a common approach to study the structure of groups by
investigating how they act on geometric and combinatorial objects, e.g.,
trees or buildings.
After briefly introducing the two structures, we will discuss a
criterion for constructing trees from buildings due to F. Haglund and F.
Paulin, and will sketch an alternative proof. Using the above-mentioned
construction, one can produce new cohomological and simplicity results
for groups acting Weyl transitively on buildings. Joint work with I.
Castellano and T. Weigel.

Supported by Mathematics Münster